Average Error: 0.2 → 0.2
Time: 3.4s
Precision: binary64
\[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}\]
↓
\[\left(1 - \frac{0.1111111111111111}{x}\right) - \frac{\frac{y}{\sqrt{x}}}{3}\]
\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}
↓
\left(1 - \frac{0.1111111111111111}{x}\right) - \frac{\frac{y}{\sqrt{x}}}{3}
double code(double x, double y) {
	return ((double) (((double) (1.0 - ((double) (1.0 / ((double) (x * 9.0)))))) - ((double) (y / ((double) (3.0 * ((double) sqrt(x))))))));
}
↓
double code(double x, double y) {
	return ((double) (((double) (1.0 - ((double) (0.1111111111111111 / x)))) - ((double) (((double) (y / ((double) sqrt(x)))) / 3.0))));
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.2
Target0.2
Herbie0.2
\[\left(1 - \frac{\frac{1}{x}}{9}\right) - \frac{y}{3 \cdot \sqrt{x}}\]

Derivation

  1. Initial program 0.2

    \[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}\]
  2. Using strategy rm

  3. Applied *-un-lft-identity0.2

    \[\leadsto \left(1 - \frac{1}{x \cdot 9}\right) - \frac{\color{blue}{1 \cdot y}}{3 \cdot \sqrt{x}}\]

  4. Applied times-frac0.2

    \[\leadsto \left(1 - \frac{1}{x \cdot 9}\right) - \color{blue}{\frac{1}{3} \cdot \frac{y}{\sqrt{x}}}\]
  5. Using strategy rm

  6. Applied associate-*l/0.2

    \[\leadsto \left(1 - \frac{1}{x \cdot 9}\right) - \color{blue}{\frac{1 \cdot \frac{y}{\sqrt{x}}}{3}}\]

  7. Simplified0.2

    \[\leadsto \left(1 - \frac{1}{x \cdot 9}\right) - \frac{\color{blue}{\frac{y}{\sqrt{x}}}}{3}\]

  8. Taylor expanded around 0 0.2

    \[\leadsto \left(1 - \color{blue}{\frac{0.1111111111111111}{x}}\right) - \frac{\frac{y}{\sqrt{x}}}{3}\]

  9. Final simplification0.2

    \[\leadsto \left(1 - \frac{0.1111111111111111}{x}\right) - \frac{\frac{y}{\sqrt{x}}}{3}\]

Reproduce

herbie shell --seed 2020162 
(FPCore (x y)
  :name "Numeric.SpecFunctions:invIncompleteGamma from math-functions-0.1.5.2, D"
  :precision binary64

  :herbie-target
  (- (- 1.0 (/ (/ 1.0 x) 9.0)) (/ y (* 3.0 (sqrt x))))

  (- (- 1.0 (/ 1.0 (* x 9.0))) (/ y (* 3.0 (sqrt x)))))